Lecture 8 The Meaning of Life Searching for Truth and The Stuff Primitives are Made Of and a smattering of Quantum Physics CS655 Programming Languages University of Virginia David Evans Computer Science http www cs virginia edu evans Menu An Important Scientific Discovery with major implications for Programming Languages Pictorial Calculi Searching for the Truth Token Rewards Manifest is online only today 13 Feb 2001 CS 655 Lecture 8 2 Scientific Discovery Announced over Weekend Human genome is about half as big as previously thought only about 30 000 genes Genetic code for 2 humans differs in only 2 1 million genetic letters 4 million bits 0 5 MB 13 Feb 2001 CS 655 Lecture 8 3 How big is 5 MB 1 3 of a floppy disk 1 of Windows 2000 Lecture Slides 1 2 and 3 13 Feb 2001 CS 655 Lecture 8 4 Nature vs C Microsoft Windows 2000 50M lines of C code 5GB of data Difference between Windows 2000 and Linux essentially all 50M lines 5GB Nature Human 30 000 genes 3 1B base pairs 1 5GB Difference between me and Michael Jordan 0 5MB 13 Feb 2001 CS 655 Lecture 8 5 Nature vs C The differences between any two people are at least 1000x more interesting than the differences between Linux and Windows 2000 Hence nature s programming language is 5GB 5MB 1000 10M times more expressive than C or 100 000 times more expressive than Scheme 13 Feb 2001 CS 655 Lecture 8 6 Is DNA Really a Programming Language 13 Feb 2001 CS 655 Lecture 8 7 Nerdy Linguist s Definition A description of pairs S M where S stands for sound or any kind of surface forms and M stands for meaning A theory of language must specify the properties of S and M and how they are related 13 Feb 2001 CS 655 Lecture 8 8 Programming Language Definition from Lecture 1 A description of pairs S M where S stands for sound or any kind of surface forms and M stands for meaning intended to be read and written by humans and processed by machines 13 Feb 2001 CS 655 Lecture 8 9 Stuff Programming Languages are Made Of Primitives My best guess sequence that encodes a protein Means of Combination Morphogenesis Not well understood by anyone This is where most of the 100Kx improvement over Scheme comes from Means of Abstraction DNA itself separate proteins from their encoding Genes group DNA by function sort of Chromosomes package Genes together Organisms packages for reproducing Genes 13 Feb 2001 CS 655 Lecture 8 10 Biology is becoming a subfield of Computer Science Biological mechanisms are mostly understood proteomics still has a way to go What is not understood is how those are combined to create meaning Alex Hartemink faculty candidate in Computational Biology Monday 3 30 13 Feb 2001 CS 655 Lecture 8 11 Pictorial Calculi Keenan s paper Any important pictorial calculi 13 Feb 2001 CS 655 Lecture 8 12 13 Feb 2001 CS 655 Lecture 8 13 Feynman Diagrams Pictorial calculi for understanding quantum electrodynamics Simple notations electron photon Rules for combining and manipulating that calculate electromagnetic interactions 13 Feb 2001 CS 655 Lecture 8 14 Richard Feynman 1918 1988 Nobel Prize in Physics 1965 for work stemming from Feynman Diagrams Leader in quantum computing PS2 Leader in nanotechnology Co taught computing course using prepublication Wizard book Every aspiring scientist should read Surely You re Joking Mr Feynman and What Do You Care What Other People Think 13 Feb 2001 CS 655 Lecture 8 15 Lambda Calculus Summary so Far Rules for substitution Rules for reduction only reduction does real work substitution Normal form no more reductions possible On faith if you do outermost reduction first you find the normal form if there is one 13 Feb 2001 CS 655 Lecture 8 16 Lambda Calculus Intuition Lambda expression corresponds to a computation Normal form is that value of that computation But can we do useful computations without primitives 13 Feb 2001 CS 655 Lecture 8 17 In search of the truth What does true mean True is something that when used as the first operand of if makes the value of the if the value of its second operand if T M N M 13 Feb 2001 CS 655 Lecture 8 18 Don t search for T search for if T xy x F xy y if pca pca 13 Feb 2001 CS 655 Lecture 8 19 Finding the Truth T xy x F xy y if pca pca Is the if necessary if T M N pca pca xy x M N ca x y x ca M N x y x M N y M N M Prakash s proof messed this up p 5 13 Feb 2001 CS 655 Lecture 8 20 and and or and xy if x y F or xy if x T y 13 Feb 2001 CS 655 Lecture 8 21 What is three ness trois 3 III 13 Feb 2001 CS 655 Lecture 8 22 Meaning of Numbers Three ness is something who s successor is four ness Three ness is something who s predecessor is two ness Zero is special It has a successor one ness but no predecessor 13 Feb 2001 CS 655 Lecture 8 23 Meaning of Numbers pred succ N N succ pred N N succ pred succ N succ N zero Zero T zero succ Zero F zero pred succ Zero T 13 Feb 2001 CS 655 Lecture 8 24 Is this enough Can we define add with pred succ zero and Zero add xy if zero x y add pred x succ y 13 Feb 2001 CS 655 Lecture 8 25 Can we define lambda expressions that behave like Zero zero pred and succ Hint what if we had cons and cdr 13 Feb 2001 CS 655 Lecture 8 26 Numbers are Lists zero x null x pred x cdr x succ x cons F x 13 Feb 2001 CS 655 Lecture 8 27 Cons and car cons xy z z xy car p p T car cons M N p p T xy z z xy M N T xy z z xy M N T z z M N M 13 Feb 2001 CS 655 Lecture 8 28 Cdr too cons xy z z xy car p p T cdr p p F cdr cons M N p p F xy z z xy M N F xy z z xy M N F z z M N N 13 Feb 2001 CS 655 Lecture 8 29 Null and null Null p p null x x T null Null x x T p p p p T T 13 Feb 2001 CS 655 Lecture 8 30 null cons Null Null x x T xy z z xy p p p p x x T z z p p p p z z p p p p T T p p p p xy x p p p p p p T but is it equivalent to F Figure it out or what I did wrong for a token reward 13 Feb …